2023

Topics of Space-Time Modeling

Name: Topics of Space-Time Modeling
Code: MAT11708D
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area: Mathematics

Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial

Sustainable Development Goals

Learning Goals

It is intended to provide a several set of statistical techniques for the identification of various temporal and spatial patterns of a given phenomenon that evolve over time, space or space-time and, depending on this identification and the objectives of the analysis, study stochastic models suited to the characteristics of the data and the objectives of their study.
At the end of the course, the student will:
- have acquired fundamental theoretical concepts on time series analysis and spatial process analysis;
- be able to apply appropriate mathematical models for time series modelling (univariate and linear), spatial process analysis techniques (point processes and continuous) and clustering analysis techniques;
- be able to use the appropriate software correctly;
- have acquired competence to undertake autonomous study of other models, appropriate for solving practical cases that students may encounter in the future.

Contents

1. Brief review of the essential concepts of Stochastic processes.
2. Temporal linear models: SARIMA model
3. Spatial point processes
4. Continuous spatial models: kriging and co-kriging spatial interpolation methods
5. Spatial clustering analysis
6. Analysis of time series and spatial data using the software R.

Teaching Methods

Theoretical-practical classes predominantly taught on the board, supported by e-learning tools and use of slides.
Introduction of theoretical concepts using examples of application in different areas, seeking to show the relevance of syllabus.
Exercises focusing on solving real problems to develop the taste and interest in the discipline and show its usefulness. Motivate attendance and the student's ongoing work.
Evaluation:
Continuous evaluation: individual homeworks (100%).
Evaluation under examination: a final exam (30%) and individual homeworks (70%).

Assessment

 Continuous evaluations with practical and/or theoretical works.

Recommended Reading

1. Barnett V. (2004). Environmental Statistics: Methods and Applications, (Wiley Series in Probability and Statistics). John Wiley & Sons. ISBN-13: 9780471489719


2. Shumway, R. H. e Stofer, D. S. (2006). Time Series Analysis and Its Applications: with R examples, 2ª ed. Springer.


3. Soares, A. (2000). Geoestatística para as Ciências da Terra e do Ambiente. IST Press, Lisboa.


4. Sprent, P. e Smeeton N.C. (2001). Applied Nonparametric Statistical Methods. Chapman & Hall/CRC.


5. Vidakovic, B. (1999). Statistical Modeling by Wavelets. Wiley Series in Probability and Statistics, Wiley, New York.


6. Webster, R e Oliver, M. A. (2001). Geostatistics for Environmental Scientists. J. Wiley & Sons, New York.

Teaching Staff

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